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If you need a index or not depends on the query you want to fire on your data.
If you have a lot of queries e.g. where you have ProgrammeTypeIdCalculated in your WHERE statements or ORDER BY clauses, then it make sense to set a index on this column.

Edit: Removed my first sentence. FK need to add constraint. I was wrong. Index need to be added (tho my migrations always do it so I checked it wrong.
So to the answer: Check the profiler and set indexes as you need depending on your queries.